Select The Correct Answer.A Company Manufactures Computers. Function { N(t)$}$ Represents The Number Of Components That A New Employee Can Assemble Per Day. Function { E(t)$}$ Represents The Number Of Components That An Experienced
Introduction
In a manufacturing company, the efficiency and productivity of employees play a crucial role in determining the overall output. When it comes to assembling components, new employees and experienced employees have different capabilities. The functions {N(t)$}$ and {E(t)$}$ represent the number of components that a new employee and an experienced employee can assemble per day, respectively. In this article, we will delve into the world of mathematics and explore the differences between these two functions.
The Function {N(t)$}$
The function {N(t)$}$ represents the number of components that a new employee can assemble per day. This function is typically represented as a linear function, which means that the number of components assembled by a new employee increases at a constant rate. The function can be represented as:
where {m$}$ is the slope of the function, representing the rate at which the number of components increases, and {b$}$ is the y-intercept, representing the initial number of components assembled by the new employee.
The Function {E(t)$}$
The function {E(t)$}$ represents the number of components that an experienced employee can assemble per day. This function is typically represented as a quadratic function, which means that the number of components assembled by an experienced employee increases at a decreasing rate. The function can be represented as:
where {a$}$ is the coefficient of the quadratic term, representing the rate at which the number of components increases, {b$}$ is the coefficient of the linear term, representing the initial number of components assembled by the experienced employee, and {c$}$ is the constant term, representing the minimum number of components assembled by the experienced employee.
Comparing the Functions
When comparing the functions {N(t)$}$ and {E(t)$}$, we can see that the number of components assembled by a new employee increases at a constant rate, while the number of components assembled by an experienced employee increases at a decreasing rate. This means that the experienced employee will eventually reach a plateau, where the number of components assembled per day will remain constant.
Graphical Representation
To better understand the differences between the functions {N(t)$}$ and {E(t)$}$, let's represent them graphically. The graph of the function {N(t)$}$ will be a straight line, while the graph of the function {E(t)$}$ will be a parabola.
Example
Suppose we have a manufacturing company that produces computers. The function {N(t)$}$ represents the number of components that a new employee can assemble per day, while the function {E(t)$}$ represents the number of components that an experienced employee can assemble per day. If the function {N(t)$}$ is represented as:
and the function {E(t)$}$ is represented as:
then we can see that the number of components assembled by a new employee increases at a constant rate, while the number of components assembled by an experienced employee increases at a decreasing rate.
Conclusion
In conclusion, the functions {N(t)$}$ and {E(t)$}$ represent the number of components that a new employee and an experienced employee can assemble per day, respectively. The function {N(t)$}$ is typically represented as a linear function, while the function {E(t)$}$ is typically represented as a quadratic function. By comparing the functions, we can see that the number of components assembled by a new employee increases at a constant rate, while the number of components assembled by an experienced employee increases at a decreasing rate.
References
- [1] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton
- [2] "Calculus" by Michael Spivak
- [3] "Linear Algebra" by Jim Hefferon
Further Reading
- "The Mathematics of Manufacturing" by John Wiley & Sons
- "Mathematics for Engineers" by McGraw-Hill Education
- "Calculus for Scientists and Engineers" by James Stewart
Q&A: Understanding the Functions of New and Experienced Employees in a Manufacturing Company =====================================================================================
Introduction
In our previous article, we explored the functions {N(t)$}$ and {E(t)$}$ that represent the number of components that a new employee and an experienced employee can assemble per day, respectively. In this article, we will answer some frequently asked questions about these functions to help you better understand their implications in a manufacturing company.
Q: What is the difference between the functions {N(t)$}$ and {E(t)$}$?
A: The function {N(t)$}$ represents the number of components that a new employee can assemble per day, while the function {E(t)$}$ represents the number of components that an experienced employee can assemble per day. The function {N(t)$}$ is typically represented as a linear function, while the function {E(t)$}$ is typically represented as a quadratic function.
Q: Why do the functions {N(t)$}$ and {E(t)$}$ have different forms?
A: The function {N(t)$}$ has a linear form because the number of components assembled by a new employee increases at a constant rate. On the other hand, the function {E(t)$}$ has a quadratic form because the number of components assembled by an experienced employee increases at a decreasing rate.
Q: What is the significance of the slope {m$}$ in the function {N(t)$}$?
A: The slope {m$}$ in the function {N(t)$}$ represents the rate at which the number of components increases. A higher slope indicates that the number of components increases at a faster rate.
Q: What is the significance of the coefficient {a$}$ in the function {E(t)$}$?
A: The coefficient {a$}$ in the function {E(t)$}$ represents the rate at which the number of components increases. A higher coefficient indicates that the number of components increases at a faster rate.
Q: How do the functions {N(t)$}$ and {E(t)$}$ affect the productivity of a manufacturing company?
A: The functions {N(t)$}$ and {E(t)$}$ can significantly affect the productivity of a manufacturing company. The function {N(t)$}$ can help the company to determine the number of components that a new employee can assemble per day, while the function {E(t)$}$ can help the company to determine the number of components that an experienced employee can assemble per day.
Q: How can the functions {N(t)$}$ and {E(t)$}$ be used in real-world applications?
A: The functions {N(t)$}$ and {E(t)$}$ can be used in various real-world applications, such as:
- Determining the number of components that a new employee can assemble per day
- Determining the number of components that an experienced employee can assemble per day
- Optimizing the production process to maximize productivity
- Determining the training requirements for new employees
Q: What are some common mistakes to avoid when using the functions {N(t)$}$ and {E(t)$}$?
A: Some common mistakes to avoid when using the functions {N(t)$}$ and {E(t)$}$ include:
- Assuming that the functions are linear or quadratic without verifying the data
- Failing to account for the initial number of components assembled by the employee
- Failing to account for the rate at which the number of components increases
- Failing to consider the impact of experience on the number of components assembled per day
Conclusion
In conclusion, the functions {N(t)$}$ and {E(t)$}$ are essential tools for determining the number of components that a new employee and an experienced employee can assemble per day, respectively. By understanding the differences between these functions and their implications in a manufacturing company, you can optimize the production process to maximize productivity and improve the overall efficiency of your company.
References
- [1] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton
- [2] "Calculus" by Michael Spivak
- [3] "Linear Algebra" by Jim Hefferon
Further Reading
- "The Mathematics of Manufacturing" by John Wiley & Sons
- "Mathematics for Engineers" by McGraw-Hill Education
- "Calculus for Scientists and Engineers" by James Stewart